Is it somehow possible to trigger publishing of the item via Sitecore item web api?
I found how to get items and similar things, but can't find the way to publish it.
For instance, to get an item I would write something like that:

What would be a syntax to publish this item from Master to Web database via item WebAPI?

PS. We use Sitecore 7.5
Here it's said that I would need to create a custom action in a controller: publish item remotely using c#
Is there simplier approach? I just need to trigger this publication once to fix some bad data in our database and then forget about that script.

If you have access to the CM why would you need a script for that? If you need to publish multiple items only once, you can use Sitecore PowerShell Extensions - doc.sitecorepowershell.com.
– Tamás TárnokJan 11 at 10:21

Yeah, I know about PowerShell Extension. Don't really like that idea, because it would require installation on Production environment which could create too much bureaucracy which I don't like...
– and85Jan 11 at 10:38